# On the inverse source identification problem in L ∞ for fully nonlinear elliptic PDE

Ayanbayev, B. and (2021) On the inverse source identification problem in L ∞ for fully nonlinear elliptic PDE. Vietnam Journal of Mathematics, 49 (3). pp. 815-829. ISSN 2305-2228

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To link to this item DOI: 10.1007/s10013-021-00515-6

## Abstract/Summary

Abstract: In this paper we generalise the results proved in N. Katzourakis (SIAM J. Math. Anal. 51, 1349–1370, 2019) by studying the ill-posed problem of identifying the source of a fully nonlinear elliptic equation. We assume Dirichlet data and some partial noisy information for the solution on a compact set through a fully nonlinear observation operator. We deal with the highly nonlinear nonconvex nature of the problem and the lack of weak continuity by introducing a two-parameter Tykhonov regularisation with a higher order L2 “viscosity term” for the L∞ minimisation problem which allows to approximate by weakly lower semicontinuous cost functionals.

Item Type: Article Yes Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics 99741 Original Article, Regularisation strategy, Tykhonov regularisation, Inverse source identification problem, Fully nonlinear elliptic equations, Calculus of Variations in L∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$L^{\infty }$\end{document}, 35R25, 35R30, 35J60, 35J70 Springer Singapore